A US-backed Syrian militia has said it has fully captured Syria's Raqqa from the Islamic State (IS) group, after months of fighting to take control of the city.

A witness told Reuters that fighting had appeared to be almost at an end with only sporadic bursts of gunfire. Militia fighters celebrated in the streets, chanting slogans from vehicles and raised a flag inside the Raqqa stadium.

The UK-based Syrian Observatory for Human Rights said that more than 3,000 were killed during the battle in Raqqa, including 1,130 civilians in more than four months.

A spokesperson for the monitoring group told AFP that months of bombardment from the US-led coalition on the former IS stronghold had killed "270 children and 2,120 combatants".

But the US military said that it could only confirm that about 90 percent of the city had been retaken.

Colonel Ryan Dillon, a spokesman for the US-led coalition fighting IS, said that about 100 fighters still remained in Raqqa and he expected the SDF to face resistance from remnants of militant group.

"We are aware of the reports that ISIS has been defeated in Raqqa," Dillon said, using an acronym for Islamic State.

"However, clearance operations continue and we expect our Syrian Democratic Force partners to hit pockets of resistance as the final parts of the city is cleared," Dillon said.

He said that in the past few days, about 1,300 civilians had been "assisted to safety" by the SDF and about 350 Islamic State fighters had surrendered in Raqqa.

The public square where IS militants carried out beheadings has also been captured by Syrian Democratic Forces as the last remaining IS militants flee Raqqa.

The site was captured after a bloody battle overnight on Monday to recapture al-Naim ("paradise") square, used by the militant group to stage victory parades, and which later became the venue for public executions.

A senior Kurdish commander told the AP news agency that his SDF fighters had not yet seen the condition of the square but called its capture symbolic.

"The group showed off its might in this square. Now it is broken and is chased out of the heart of its alleged capital," the commander said.

Aid agencies have warned of a "humanitarian crisis" inside Raqqa after the city was levelled to the ground.

"The military offensive in Raqqa may be coming to an end, but the humanitarian crisis is greater than ever," Sonia Khush who works for Save the Children said in a statement.

Khush said that the reconstruction effort would require massive investment and that funding is also needed to bring children back to school.

"Many [children] are plagued by nightmares from witnessing horrific violence and will have extensive psychological support."

The takeover comes after rapid advances against IS in the city, and deals agreed between the SDF and Syrian fighters within IS to leave the city in return for the safe passage of remaining civilians.

Foreign IS militants have been refused similar agreements, and SDF commanders estimated on Monday there were fewer than 300 left in Raqqa.

The SDF also said on Tuesday they had captured Raqqa's state hospital, one of the last redoubts of IS.